Electroacoustic transducers are commonly used in a variety of underwater applications, including acoustical communication, underwater survey, and sound detection. Such transducers are commonly made from a piezoelectric element which operates to convert between mechanical energy in the form of a compressive, expansive, or shear force and an electrical potential which appears across different parts of the piezoelectric element. Thus, when a piezoelectric element vibrates under the force of an acoustic wave, a resulting alternating electric potential indicative of the acoustic wave is induced across the piezoelectric element. Conversely, an alternating electric potential applied across a piezoelectric element will cause the piezoelectric element to vibrate, thereby producing an acoustic wave at a frequency dependent upon the frequency of the applied electric potential and the characteristics of the piezoelectric element. In this way, electroacoustic transducers can be used to send and/or receive acoustical information.
Piezoelectric elements of varying geometries can be utilized for electroacoustic conversion. See, for example, U.S. Pat. No. 3,972,018, issued Jul. 17, 1976 to D.J. Erickson. One type of piezoelectric element commonly used is a hollow piezoelectric cylinder having electrodes on its inner and outer circumferential surfaces. These cylinders operate to convert between electric potential and radial movement of the cylinder. However, these cylinders have certain problematic characteristics that reduce their suitability for underwater communication and reconnaissance. For instance, piezoelectric materials typically have a low tensile strength and can therefore break apart when subject to the large driving voltages often needed for generating large acoustical waves. This aspect of their operation is addressed in U.S. Pat. Nos. 4,220,887, issued Sep. 2, 1980 to H.W. Kompanek, 4,156,824, issued May 29, 1979 to E.A. Pence, Jr., 3,716,828, issued Feb. 13, 1973 to F. Massa, and 3,474,403, issued Oct. 21, 1969 to F. Massa et al. Typically, the risk of breakage of the piezoelectric cylinder is reduced or eliminated by limiting radial expansion of the cylinder through the use of a " pre-stress" wrap secured about the outer periphery of the cylinder. This pre-stress wrap provides a static, inwardly radial force on the cylinder.
Another problem encountered with the use of piezoelectric cylinders is that the conversion between electrical and acoustical energy is somewhat low at all but a number of resonant frequencies. The cylinder therefore has a high "Q" at these resonant frequencies. The cylinder has a number of resonant frequencies associated with it, including a wall thickness resonant frequency (the frequency at which the thickness of the cylinder wall undergoes its maximum oscillations), a length mode resonant frequency (the frequency at which the cylinder undergoes its maximum lengthwise oscillations), a radial mode resonant frequency (the frequency at which the diameter of the cylinder undergoes its maximum oscillations), and a cavity mode resonant frequency (a frequency dependent upon the length and diameter of the cylinder and the velocity of sound in the fluid disposed within the cylinder). Therefore, acoustical communication and detection by a simple piezoelectric cylinder is normally limited to a narrow band of frequencies located about these resonant frequencies.
The radial mode resonant frequency can be calculated according to the formula: ##EQU1## where a is the mean radius of the cylinder, Y is Young's modulus of the ceramic, .sigma. is Poisson's ratio of the ceramic, and p is the density of the ceramic material. This resonant frequency can be raised or lowered by decreasing or increasing, respectively, the diameter of the piezoelectric cylinder. Another means for lowering the radial mode resonant frequency is to form a composite transducer by adding inertial masses about the outer periphery of the cylinder. See, for example, U.S. Pat. Nos. 4,823,327, issued Apr. 18, 1989 to H. Hilmers, 3,111,595, issued Nov. 19, 1963 to M.C. Junger, and 2,775,749, issued Dec. 25, 1956 to H. Sussman.
Alternatively, the aforementioned patent to Pence, Jr. purports to provide a composite transducer which lowers the radial mode resonant frequency several octaves below that of the cylinder alone. The transducer includes a cylindrical shell that is fitted over and which extends beyond the piezoelectric cylinder. The shell is slotted for part of its length from each end to form "leaves" which flex with radial expansion and contraction of the cylinder. One disadvantage of this device is that the free ends of the leaves can oscillate out of phase with the oscillations of the cylinder at certain frequencies, thereby causing phase-inverted oscillations that dampen the response of the transducer at those frequencies. The primary phase-inverted oscillation frequency can be predicted by the formula: ##EQU2## where c.sub.s is the sound velocity of the shell material and L is the length of the slotted shell.
The cavity mode resonant frequency is typically lower than the radial mode resonant frequency and can be calculated according to the formula: ##EQU3## where L is the length of the ceramic cylinder, r is the inside radius of the ceramic, .alpha. is a frequency factor dependent upon the ratio of L to r, and ##EQU4## in which B is the bulk modulus of water, c is the speed of sound in water, and t is the wall thickness of the cylinder.
Regardless of the frequency at which such transducers undergo their various resonances, it would be advantageous to broaden the frequency range over which there is efficient electroacoustical conversion. It would also be advantageous to maintain the Q of the transducer small across the broadened frequency range. This would permit the transducer to transmit and receive a wider range of acoustical information, thereby improving the operation of the transducers for their intended use as well as making any one transducer suitable for a broader range of applications.